In my first relationship and already having problems. Help?

2 weeks ago, my friend was in a bad mood and I accidentally said something stupid to her to piss her off. I found out she was in a bad mood because her ex broke up the relationship and doesn't want anything to do with her anymore.
Soon enough the week after they broke up, she came and asked me "If i gave you a chance what would it be?"
and as i honest as i was I told her "I want to be with you because i still have feelings for you"
Sure enough we were together.
The first week we were together, it was fine.
The second week ibecame a roller coaster of emotions for me.
Tuesday of the 2nd Week , i asked her if we could hang once in a while during lunch but she said she rather hang with her best friend at lunch (girl bestie). i didn't want to argue so i let it slide b/c if i know one thing, you can't win a fight against the woman you care for. I was depressed b/c all i wanted was to hang with her alone during lunch. Not much to ask when it's just once in a while.
On Thursday. i saw her sad while she was walking with her bestie , i said hi with a smile but she never did smile back or said hi at all. I went to check on her and she showed a blank face saying she was fine. Me , her and her Bestie were at a club meeting. At the end of the meeting, i checked my phone really quick and soon enough. My GF just left without me along with her bestie. I was pretty pissed off at her, but i didn't want to argue knowing that it has been ONLY A WEEK that i've been in this relationship. I talked to her online, saying how we should communicate and needs to open up. She told me she wants to take care of it herself. It was dandy till i pissed her off jokingly that my sister can act as her senior friend because i invited her to go Kayaking with me even though i did know that her parents don't let her out. In my defense, she was overreacting.
On Friday , i made it up to her. I gave her, her early birthday present. She smiled, she had a bad day that day and it made up her day. I hugged her goodbye knowing that we wouldn't have contact that much during spring break and (i think) she made lip smack so i guess she was trying to kiss me on the cheeks? At night i talked to her online, she needed more things to watch since her internet isn't working. I said i would bring it to her but she was uncomfortable of me knowing where she lives. I said fine , i would just give it to her bestfriend since they hang out a lot.

At this point, i have no clue what i'm doing anymore. I'm the one who always starts the conversation , the one who comes to her , the one who's trying to make it work.
I did talk to her twice about communication but i don't know, she doesn't seem to get it or something.
I want her to actually share a bit of emotion with me, talking to me , comming to me once in a while?
How do i make this work?

Note.
- I'm a Junior in High School and She's A Freshman
- She would tell me her negatives like how she's bipolar , gets jealous easily , doesn't like to be touched when she's pissy ect.
- Her Ex cheated on her 5 times and it was a Long Distance Relationship.
- She hangs with her Best Friend(girl) more than me because they were together more
- I always start the conversation with her but at least she responds back .
- I can't hang with her during weekends or holiday or spring/summer/winter/ break because of her strict parents. Only after school we could hang out.
- This is my first legit Relationship

You are not in a relationship with this girl. She's too young to even know what that means, at least that's how she is acting. She has no idea what she wants and you are pretty much wasting your time on her.